Abstract
All differential equations students have encountered eigenvectors and eigenvalues in their study of systems of linear differential equations. The eigenvectors and phase plane solutions are displayed in a Cartesian plane, yet a geometric understanding can be enhanced, and is arguably better, if the system is represented in polar coordinates. A consequence of using the polar form is that the geometric characteristics of centres and spirals are immediately identified, while the features of saddles and nodes are also made clear.
Disclosure statement
No potential conflict of interest was reported by the author.